Problem: Solve for $x$ and $y$ using elimination. ${3x-2y = -12}$ ${-5x+5y = 35}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $3$ ${15x-10y = -60}$ $-15x+15y = 105$ Add the top and bottom equations together. $5y = 45$ $\dfrac{5y}{{5}} = \dfrac{45}{{5}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {3x-2y = -12}\thinspace$ to find $x$ ${3x - 2}{(9)}{= -12}$ $3x-18 = -12$ $3x-18{+18} = -12{+18}$ $3x = 6$ $\dfrac{3x}{{3}} = \dfrac{6}{{3}}$ ${x = 2}$ You can also plug ${y = 9}$ into $\thinspace {-5x+5y = 35}\thinspace$ and get the same answer for $x$ : ${-5x + 5}{(9)}{= 35}$ ${x = 2}$